Jekyll2019-12-12T15:51:04+00:00https://math.virginia.edu/feed.xmlMathematics at the University of VirginiaOfficial website of Department of Mathematics at the University of VirginiaUVA MathGreg Lawler — Virginia Mathematics Lectures, February 12-14, 20202019-12-07T00:00:00+00:002019-12-07T00:00:00+00:00https://math.virginia.edu/ims/lectures/greg-lawler<h5 class="mt-1 mb-4"><a href="https://math.uchicago.edu/~lawler/">Greg Lawler</a> (University of Chicago)</h5>
<ul>
<li>Lecture 1 - “<strong>Random walks: simple and self-avoiding</strong>”. Wednesday, February 12, 2020. Time and location TBA</li>
<li>Lecture 2 - “<strong>Conformal invariance and two-dimensional critical phenomenon</strong>”. Thursday, February 13, 2020. Time and location TBA</li>
<li>Lecture 3 - “<strong>Loop measures and the loop-erased random walk</strong>”. Friday, February 13, 2020. Time and location TBA</li>
</ul>
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<h3 id="lecture-1-random-walks-simple-and-self-avoiding">Lecture 1. Random walks: simple and self-avoiding</h3>
<p>The most common model for random behavior is the “drunkard’s walk” where at each time an individual chooses their step from some probability distribution. I will review this and then discuss what happens when one puts some constraints on the walker to try to avoid places already visited. We will see the relationship between the “fractal dimension” of the random path and the ambient dimension in which it lives.</p>
<h3 id="lecture-2-conformal-invariance-and-two-dimensional-critical-phenomenon">Lecture 2. Conformal invariance and two-dimensional critical phenomenon</h3>
<p>It was predicted by theoretical physicists that lattice models from equilibrium statistical physics “at criticality” in two dimensions have limits that are conformally invariant. There has been an incredible amount of work in the last twenty years making these ideas precise and rigorous and I will survey this work. The starting point was the development of the Schramm-Loewner evolution (SLE) which I will define.</p>
<h3 id="lecture-3-loop-measures-and-the-loop-erased-random-walk">Lecture 3. Loop measures and the loop-erased random walk</h3>
<p>This talk will focus on two related models: loop measures and the loop-erased random walk which are closely related to uniform spanning trees and describe some relatively recent work in this area in dimensions two, three, and four.</p>
<p><br /><br /></p>
<p><a href="https://math.virginia.edu/ims/lectures">Virginia Mathematics Lectures archive</a></p>UVA MathGreg Lawler (University of Chicago) Lecture 1 - “Random walks: simple and self-avoiding”. Wednesday, February 12, 2020. Time and location TBA Lecture 2 - “Conformal invariance and two-dimensional critical phenomenon”. Thursday, February 13, 2020. Time and location TBA Lecture 3 - “Loop measures and the loop-erased random walk”. Friday, February 13, 2020. Time and location TBARepresentations of Algebraic Groups and Quantum Groups2019-11-23T00:00:00+00:002019-11-23T00:00:00+00:00https://math.virginia.edu/2019/11/repth-workshop-2020<p>Department of Mathematics and
Institute of Mathematical Science
will hold the workshop on
<a href="https://math.virginia.edu/ims/rt-workshop-spring-2020/">Representations of Algebraic Groups and Quantum Groups</a>.</p>
<p>The workshop is followed by
an AMS special session on “<a href="http://www.ams.org/meetings/sectional/2273_program_ss13.html#title">Representations of algebraic groups and quantum groups: a tribute to Cline-Parshall-Scott (CPS)</a>”, Charlottesville, Virginia, March 13-15, 2020</p>
<p>Organizers: <a href="https://www.math.uga.edu/directory/people/daniel-k-nakano">Dan Nakano (University of Georgia)</a>
<span style="white-space:nowrap"><a href="mailto:asr3x@virginia.edu"><span class="fa fa-envelope" aria-hidden="true" style="font-size:0.8em"></span></a> <a href="http://pi.math.virginia.edu/Faculty/Rapinchuk/">Andrei Rapinchuk</a></span>
<span style="white-space:nowrap"><a href="mailto:ww9c@virginia.edu"><span class="fa fa-envelope" aria-hidden="true" style="font-size:0.8em"></span></a> <a href="http://people.virginia.edu/~ww9c/">Weiqiang Wang</a></span></p>UVA MathDepartment of Mathematics and Institute of Mathematical Science will hold the workshop on Representations of Algebraic Groups and Quantum Groups. The workshop is followed by an AMS special session on “Representations of algebraic groups and quantum groups: a tribute to Cline-Parshall-Scott (CPS)”, Charlottesville, Virginia, March 13-15, 2020 Organizers: Dan Nakano (University of Georgia) Andrei Rapinchuk Weiqiang WangVirginia Math Bulletin, November 20192019-11-10T00:00:00+00:002019-11-10T00:00:00+00:00https://math.virginia.edu/2019/11/bulletin<p>Presenting the sixth issue of the Department newsletter: <a href="https://math.virginia.edu/allnews/virginia-math-bulletin/Bulletin2019.pdf">2019 Virginia Math Bulletin</a>.</p>
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<h3 class="mt-5 mb-3">View from the Chair</h3>
<p>The last year was an eventful one for mathematics at UVa. We had a big year in terms of new tenured/tenure-track faculty. Two new assistant professors, Evangelia Gazaki and You Qi, joined our ranks, and we were also very fortunate to be able to recruit Ken Ono as the Thomas Jefferson Professor of Mathematics. Evangelos Dimou is joining our general faculty team that is focused on renewing our calculus program. Read ahead for profiles of all of our new faculty, as well as our new postdocs Bruno Braga, Anna Pun, and Charlotte Ure. It is particularly meaningful for me as chair to see the new faculty begin to shape the department and to assume their role as mentors for the next generation of mathematicians.</p>
<p>This year, we are gearing up for a major expansion of our postdoc program. One component of this relates to our ambitious plans to extend our smaller-class, interactive model for calculus to our applied calculus sequence. Smaller class sizes means more instructors, and additional postdocs will help with that. The other component relates to a large five-year NSF award to our topology-geometry group, which includes the hiring of two new postdocs each year for three years. Read ahead for an article on the new RTG grant (Research Training Grant).</p>
<p>Other highlights of this edition of the Virginia Math Bulletin include an article by Weiqiang Wang on his recent landmark work on Lie theory with his former student, Huanchen Bao, articles on undergraduate research projects conducted in the last year, and articles on activities of our AWM chapter (American Women in Mathematics). You can read about our Virginia Math Lectures by Fields medalist Andrei Okounkov and Pólya Prize winner Van Vu. There is an article about the career of Nat Martin, one of our emeritus faculty, who passed away this past year. He joined the department in 1959 and was a fixture here for nearly 40 years.</p>
<p>We are just now finishing up an intensive period of renovations to Kerchof Hall,
including a renewal of our lounge and kitchen area. The Math Lounge is a dream given form, giving a place for all of us to socialize, meet, and interact. I hope that whenever you are in town, you will take the time to visit and see for yourself by joining us for one of our Tuesday/ Thursday teas. Or should I say coffees? We are testing Rényi’s claim that a mathematician is a device for turning coffee into theorems.</p>
<p>I am particularly grateful for the support of the larger community of graduates and former members of this department. We are looking forward to another exciting year in the department, with new discoveries, involving our very talented graduate and undergraduate students, post-doctoral fellows, and faculty. Please enjoy this newsletter and let us know what you think. We hope you will stay in touch and I welcome your comments and questions.</p>
<p><a href="https://math.virginia.edu/people/ji2k/">John Imbrie</a></p>
<p>Professor of Mathematics, Chair</p>
<h3 id="continue-reading-in-pdf"><a href="https://math.virginia.edu/allnews/virginia-math-bulletin/Bulletin2019.pdf">Continue reading in PDF</a></h3>UVA MathPresenting the sixth issue of the Department newsletter: 2019 Virginia Math Bulletin.Huanchen Bao and Weiqiang Wang Will Receive the 2020 Chevalley Prize2019-11-07T00:00:00+00:002019-11-07T00:00:00+00:00https://math.virginia.edu/2019/11/Wang-Bao<p>The 2020 Chevalley Prize in Lie Theory will be awarded to Huanchen Bao and Weiqiang Wang for their fundamental contributions to the theory of quantum symmetric pairs.</p>
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<p>This award is based on two publications: the paper “Canonical bases arising from quantum symmetric pairs,” published in Inventiones Mathematicae, and the monograph “A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs,” published in Astérisque. In these works, Huanchen Bao and Weiqiang Wang completely extended the known theory of canonical bases from the case of quantized enveloping algebras to the case of quantum symmetric pairs.</p>
<p>In his 2015 UVa PhD thesis supervised by Wang, Huanchen Bao solved the longstanding problem of computing simple characters in the BGG category of modules over a simple Lie superalgebra g of type B/C. To that end, Bao and Wang developed a theory of canonical bases arising from quantum symmetric pairs, generalizing Lusztig’s construction.</p>
<p><a href="http://www.ams.org/tools/news?news_id=5611">http://www.ams.org/tools/news?news_id=5611</a></p>UVA MathThe 2020 Chevalley Prize in Lie Theory will be awarded to Huanchen Bao and Weiqiang Wang for their fundamental contributions to the theory of quantum symmetric pairs.Public lecture by Diane Hoffoss2019-10-13T00:00:00+00:002019-10-13T00:00:00+00:00https://math.virginia.edu/2019/10/Hoffoss-public-lecture<p>Public lecture by Prof. Diane Hoffoss (University of San Diego)
“Unfolding Humanity: Mathematics at Burning Man”
will be
on October 21 at 5:30pm in Physics Building 204. The public talk is for general audience.</p>
<p>Diane will visit UVa on October 21-22, see <a href="http://www.people.virginia.edu/~sm4cw/Diane_Hoffoss.html">here</a> for a full schedule of events and more details.</p>
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<h5 id="public-lecture-title-unfolding-humanity-mathematics-at-burning-man">Public Lecture Title: Unfolding Humanity: Mathematics at Burning Man</h5>
<p>A two-ton interactive sculpture called Unfolding Humanity came to life at Burning Man 2018, the world’s most influential large-scale sculpture showcase. Rising 12 feet tall with an 18-foot wingspan in the Nevada desert, the unfolding dodecahedron was illuminated by 16,000 LEDs, requiring 6500 person hours and $40,000 in funds. Its interior, large enough to hold 15 people, was fully lined with massive mirrors, alluding to a possible shape of our universe. The unfolding exterior points to the 500-year-old work of Albrecht Dürer, and the tantalizing open problem of discovering a geometric unfolding for every convex polyhedron. This talk outlines the journey of two mathematicians embracing the role of amateur sculpture artists.</p>
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<h5 id="geometry-seminar-title-topological-and-geometric-complexity-for-hyperbolic-3-manifolds">Geometry Seminar Title: Topological and Geometric Complexity for Hyperbolic 3-Manifolds</h5>
<p>We will introduce Scharlemann-Thompson handle decompositions of a 3-manifold, and a generalization of this which we call a graph decomposition. Using these, we define topological measures of complexity for the manifold. In the case where the manifold has additional metric structure, we use Morse and Morse-like functions to give geometric definitions of complexity as well. We will then reveal connections between these geometric and topological complexities.</p>
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<h5 id="short-bio">Short Bio:</h5>
<p>Diane Hoffoss is an Associate Professor of Mathematics at the University of San Diego with research interests in the areas of 3-manifold topology, foliations, and hyperbolic geometry. She has also worked at NASA JPL on problems involving optimizing the scheduling of communication between the Mars rovers, Mars orbiters, and the 3 Deep Space Network stations on Earth, and she has written a computer program which computes length spectra of hyperbolic manifolds which was included in the software system SnapPea.</p>
<p>She has also combined her love of the visual side of mathematics with her programming skills in the creation of several large-scale art installations at Burning Man. Most notably, she was Lead Artist and Project Co-Lead for her project Unfolding Humanity, a 12’ unfolding dodecahedron which included programmed LED animations and an interior infinity mirror room, and was Lighting Artist and Software Lead for a multimedia, 42’ diameter torus called The Journey Project.</p>UVA MathPublic lecture by Prof. Diane Hoffoss (University of San Diego) “Unfolding Humanity: Mathematics at Burning Man” will be on October 21 at 5:30pm in Physics Building 204. The public talk is for general audience. Diane will visit UVa on October 21-22, see here for a full schedule of events and more details.Upcoming mathematics competitions2019-10-01T00:00:00+00:002019-10-01T00:00:00+00:00https://math.virginia.edu/2019/10/competitions<ol>
<li>
<p>The <a href="http://intranet.math.vt.edu/people/plinnell/Vtregional/">Virginia Tech Regional Math Competition</a> will be held on Saturday, October 26, from 9am to 11:30 am. The exam will be held in Clark 101. Interested students should arrive by 8:30 am for registration formalities. No prior registration is required.</p>
</li>
<li>
<p>The <a href="https://www.maa.org/math-competitions/putnam-competition">Putnam competition</a> will be held on Saturday, December 7, from 10 am to 6 pm, with a two hour lunch break between sessions. The exam will be held in New Cabell Hall, room 323. Interested students should arrive by 9:30 am for registration formalities. No prior registration is required.</p>
</li>
</ol>
<p>Future competition announcements will be posted on the <a href="https://math.virginia.edu/undergraduate/competitions/">special page</a>.</p>UVA MathThe Virginia Tech Regional Math Competition will be held on Saturday, October 26, from 9am to 11:30 am. The exam will be held in Clark 101. Interested students should arrive by 8:30 am for registration formalities. No prior registration is required. The Putnam competition will be held on Saturday, December 7, from 10 am to 6 pm, with a two hour lunch break between sessions. The exam will be held in New Cabell Hall, room 323. Interested students should arrive by 9:30 am for registration formalities. No prior registration is required. Future competition announcements will be posted on the special page.Mid-Atlantic Topology Seminar 20192019-09-29T00:00:00+00:002019-09-29T00:00:00+00:00https://math.virginia.edu/2019/09/mid-atlantic-topology-seminar-2019<p>There will be a one day Mid-Atlantic Topology Seminar at University of Virginia on Saturday, October 26.
Speakers will be:</p>
<ul>
<li>Maria Basterra (University of New Hampshire)</li>
<li>Mona Merling (University of Pennsylvania)</li>
<li>Dylan Wilson (University of Chicago)</li>
<li>W. Stephen Wilson (Johns Hopkins University)</li>
</ul>
<p>This seminar is a regional conference with a goal of bringing together the mid-Atlantic algebraic topology community. It will also serve as one of the inaugural activities for the NSF RTG grant that the Topology and Geometry group at UVA recently received.</p>
<ul>
<li><a href="https://math.virginia.edu/geomtop/conferences/">Details and registration</a></li>
<li><a href="https://math.virginia.edu/geomtop/">Geometry and topology group page</a></li>
</ul>
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<p>All talks will be held in Clark Hall 107. Free parking is available in the C1 parking lot behind Clark Hall, next to Kerchof Hall.</p>
<h5 id="schedule">Schedule</h5>
<p>(coffee and pastries: 9-9:30)</p>
<p>9:30 – 10:30 W. Stephen Wilson (Johns Hopkins University)</p>
<p>Title: $v_n$ torsion free H-spaces</p>
<p>Abstract: For some years there have been $(k-1)$-connected irreducible H-spaces, $Y_k$, with no p-torsion
in homology or homotopy. All p-torsion free H-spacesa are products of these spaces and they show up regularly
in the literature. Boardman and I have generalized theses spaces and theorems using $(k-1)$ connected H-spaces,
$Y_k$, that have no $v_n$ torsion in homology or homotopy (to be defined). These spaces seem ripe for exploitation
in the environment of chromatic homotopy theory.</p>
<p>(break: 10:30-11)</p>
<p>11:00–12:00 Mona Merling (University of Pennsylvania)</p>
<p>Title: Spectral Mackey functors as multifunctors</p>
<p>Abstract: I will discuss a new perspective on spectral Mackey functors as multifunctors. The main application I will
talk about is the construction of a map from the suspension G-spectrum of a smooth G-manifold M to the equivariant
A-theory of M, whose fiber, on fixed points, exhibits a “tom Dieck style” splitting into stable h-cobordism spaces.<br />
This is joint work with Cary Malkiewich.</p>
<p>(lunch: 12-2)</p>
<p>2:00-3:00 Dylan Wilson (Harvard)</p>
<p>Title: Real Hochschild homology and the norm of $F_2$.</p>
<p>Abstract: We study a spectral sequence computing the homotopy fixed points of the $C_2$ action on the smash square
of $HF_2$. As an application, we give another proof of the $C_2$-Segal conjecture as well as a stronger, ‘quantitative’
variant. This is joint work with Jeremy Hahn.</p>
<p>(break: 3-3:30)</p>
<p>3:30—4:30 Maria Basterra (University of New Hampshire)</p>
<p>Title : Inverting operations in operads</p>
<p>Abstract : We describe a variant of the Dwyer-Kan hammock localization that allows us to construct a localization
for operads with respect to submonoids of one-ary operations. The construction is functorial. It associates to an
operad O and a submonoid of one-ary operations W, an operad LO and a canonical map O to LO which takes elements in W
to homotopy invertible operations.
Furthermore, we give a functor from the category of O-algebras to the category of LO-algebras satisfying an appropriate
universal property.
This is joint work with Irina Bobkova, Kate Ponto, Ulrike Tillmann and Sarah Yeakel.</p>UVA MathThere will be a one day Mid-Atlantic Topology Seminar at University of Virginia on Saturday, October 26. Speakers will be: Maria Basterra (University of New Hampshire) Mona Merling (University of Pennsylvania) Dylan Wilson (University of Chicago) W. Stephen Wilson (Johns Hopkins University) This seminar is a regional conference with a goal of bringing together the mid-Atlantic algebraic topology community. It will also serve as one of the inaugural activities for the NSF RTG grant that the Topology and Geometry group at UVA recently received. Details and registration Geometry and topology group pageThesis defense: Aleksander Morgan2019-09-15T00:00:00+00:002019-09-15T00:00:00+00:00https://math.virginia.edu/2019/09/Morgan<p><strong>Aleksander Morgan</strong> will defend the Ph.D. thesis on Thursday, September 19.
The title is</p>
<p>“<em>Bounded generation of some linear groups</em>”.</p>
<ul>
<li>Date: Thursday, September 19</li>
<li>Time: 3:30 pm</li>
<li>Place: Kerchof 317</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathAleksander Morgan will defend the Ph.D. thesis on Thursday, September 19. The title is “Bounded generation of some linear groups”. Date: Thursday, September 19 Time: 3:30 pm Place: Kerchof 317 Everyone is invited to attend.Peter Sarnak - Virginia Mathematics Lectures - November 4-6, 20192019-09-08T00:00:00+00:002019-09-08T00:00:00+00:00https://math.virginia.edu/ims/lectures/peter-sarnak<h5 class="mt-1 mb-4"><a href="https://www.math.ias.edu/people/faculty/sarnak">Peter Sarnak</a> (IAS)</h5>
<ul>
<li>Lecture 1 - “<strong>Integral Quadratic Forms and Applications</strong>”. November 4, 5-6pm, Nau 101</li>
<li>Lecture 2 - “<strong>Integer points on affine cubic surfaces</strong>”. November 5, 5-6pm, Monroe 124</li>
<li>Lecture 3 - “<strong>Applications of points on subvarieties of tori</strong>”. November 6, 5-6pm, Nau 101</li>
</ul>
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<h3 id="lecture-1-integral-quadratic-forms-and-applications">Lecture 1. Integral Quadratic Forms and Applications</h3>
<p>Quadratic Diophantine equations (sums of integer squares ) have fascinated mathematicians for centuries however even today some the finer local to global questions are not understood, and the complexity of finding solutions is challenging. We will explain and review these features and highlight some applications, for example to quantum computation with the construction of optimal universal quantum gates.</p>
<h3 id="lecture-2-integer-points-on-affine-cubic-surfaces">Lecture 2. Integer points on affine cubic surfaces</h3>
<p>A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems when the integers are replaced by integers in say a real quadratic field.</p>
<h3 id="lecture-3-applications-of-points-on-subvarieties-of-tori">Lecture 3. Applications of points on subvarieties of tori</h3>
<p>The intersection of the division group of a finitely generated subgroup of a torus with an algebraic subvariety has been understood for some time (Lang, Laurent,…). After a brief review of some of the tools in the analysis and their recent extensions (Andre’-Oort Conjectures ), we give some old and new applications; periodicity of Betti numbers, algebraicity of Painleve’ equations, and the additive structure of spectra of quantum graphs.</p>
<p><br /><br /></p>
<p><a href="https://math.virginia.edu/ims/lectures">Virginia Mathematics Lectures archive</a></p>UVA MathPeter Sarnak (IAS) Lecture 1 - “Integral Quadratic Forms and Applications”. November 4, 5-6pm, Nau 101 Lecture 2 - “Integer points on affine cubic surfaces”. November 5, 5-6pm, Monroe 124 Lecture 3 - “Applications of points on subvarieties of tori”. November 6, 5-6pm, Nau 101Lunch with Sherry Gong (UCLA)2019-09-04T10:00:00+00:002019-09-04T10:00:00+00:00https://math.virginia.edu/2019/09/sherry-gong-lunch<p>This week, the AWM met with Sherry Gong, an Assitant Adjunct Professor at UCLA.</p>
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<p>Over sandwiches, we discussed with Sherry her educational
background, from Puerto Rico to to Harvard to MIT. We learned how she competed on both the US and Puerto Rico team in the International
Mathematical Olympiad, always as one of the strongest competitors, and how she went on to coach the US Women’s team for the Girls’
Mathematical Olympiad in 2010. Sherry discussed how her personal areas of research (low dimensional topology, operator theory) in math have
been so largely determined by the mentors she could find. Gong explained the importance for her of picking good mentors as an undergrad and
graduate student, and how to go about securing a good mentor, which opened up to a general room discussion of the most aggressive/intense
moves people had made to try to secure a mentor. We rounded out the meeting by discussing the process of applying in the field, and how to
pick research projects, make connections, and send emails to secure your own chance of getting your CV considered.</p>
<p>Follow us on <a href="https://www.facebook.com/AWMatUva">FB</a> to stay updated on AWM events and posts!</p>
<p>By Mia Shaker</p>UVA MathThis week, the AWM met with Sherry Gong, an Assitant Adjunct Professor at UCLA.